Projection schemes for fluid flows through a porous interface

Alfonso Caiazzo; Miguel Angel Fernández; Jean-Frédéric Gerbeau; Vincent Martin

Projection schemes for fluid flows through a porous interface

Alfonso Caiazzo ^{1, *} Miguel Angel Fernández ^{1, *} Jean-Frédéric Gerbeau ^{1, *} Vincent Martin ^{2, *}

* Corresponding author

1 REO - Numerical simulation of biological flows

LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6

2 UTC - Université de Technologie de Compiègne

Abstract : This paper presents a numerical method to simulate an incompressible fluid through an immersed porous interface. The interface is modeled by a surface measure term in the Navier-Stokes equations and it is characterized by a resistance parameter. This approach can be used for example to model valves or to simulate blood flood through an immersed stent. Starting from a monolithic formulation proposed recently, a fractional step algorithm is derived. The difficult point is that this formulation is singular when the resistance vanishes, which can be a serious issue in some applications. We show that an appropriate Nitsche's treatment of the interface condition fixes this problem and ensures uniform energy stability in time, for any non-negative value of the resistance. The theoretical stability and convergence results are illustrated with numerical experiments

Document type :

Journal articles

Domain :

Mathematics [math] / Numerical Analysis [math.NA]

Life Sciences [q-bio] / Bioengineering

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https://hal.inria.fr/inria-00462103
Contributor : Miguel Angel Fernández <>
Submitted on : Monday, March 8, 2010 - 5:30:07 PM
Last modification on : Wednesday, May 15, 2019 - 3:48:20 AM
Long-term archiving on : Friday, June 18, 2010 - 8:06:14 PM

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